Stress in torsion springs is due to bending, and for round wire is given by:
S = (32M / ∏d3) KB
During elastic deflection of a curved beam, the neutral axis shifts toward the center of curvature, causing higher stress at the inner surface than the outer. Wahl has calculated the stress correction factor as the inside diameter (I.D.) of a round wire torsion spring as:
KBID = (4C - C - 1) / 4C (C - 1)
A convenient approximation for engineering calculations is:
KBID = (4C - 1) / (4C - 4)
KBOD = (4C + 1) / (4C + 4)
At low indexes, stress is significantly higher on the inner surface than the outer. These factors are useful to determine the stress range for cyclic applications and the set point for fully stress-relieved springs in static applications. A stress correction factor of one is recommended to determine the set point of torsion springs that have favorable residual stresses induced by yielding during forming. Yielding results in a more uniform stress distribution over the round cross section. Therefore, the actual stress distribution over the round cross section. Therefore, the actual stress correction factor approaches the recommended value of one.
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